Theory of high-harmonic generation by low-frequency laser fields

Harnessing attosecond science in the quest for coherent X-rays

Modern laser technology has revolutionized the sensitivity and precision of spectroscopy by providing coherent light in a spectrum spanning the infrared, visible, and ultraviolet wavelength regimes. However, the generation of shorter-wavelength coherent pulses in the x-ray region has proven much more challenging. The recent emergence of high harmonic generation techniques opens the door to this possibility. Here we review the new science that is enabled by an ability to manipulate and control electrons on attosecond time scales, ranging from new tabletop sources of coherent x-rays to an ability to follow complex electron dynamics in molecules and materials. We also explore the implications of these advances for the future of molecular structural characterization schemes that currently rely so heavily on scattering from incoherent x-ray sources.

Ultrafast electronuclear dynamics of H(2) double ionization

The ultrafast electronic and nuclear dynamics of H(2) laser-induced double ionization is studied using a time-dependent wave packet approach that goes beyond the fixed nuclei approximation. The double ionization pathways are analyzed by following the evolution of the total wave function during and after the pulse. The rescattering of the first ionized electron produces a coherent superposition of excited molecular states which presents a pronounced transient H(+)H(-) character. This attosecond excitation is followed by field-induced double ionization and by the formation of short-lived autoionizing states which decay via double ionization. These two double ionization mechanisms may be identified by their signatures imprinted in the kinetic-energy distribution of the ejected protons.

Probing orbital structure of polyatomic molecules by high-order harmonic generation

The effects of electronic structure and symmetry are observed in laser driven high-order harmonic generation for laser aligned conjugated polyatomic molecular systems. The dependence of the harmonic yield on the angle between the molecular axis and the polarization of the driving laser field is seen to contain the fingerprint of the highest occupied molecular orbitals in acetylene and allene, a good quantitative agreement with calculations employing the strong field approximation was found. These measurements support the extension of the recently proposed molecular orbital imaging techniques beyond simple diatomic molecules to larger molecular systems.

High harmonic generation and the role of atomic orbital wave functions

High harmonic spectra were recorded from different rare-gas atoms under identical experimental conditions. It is shown that although each atom's spectrum is different, the differences are due almost entirely to the orbital influence in the recombination step. The amplitude of the continuum electron wave packet versus kinetic energy is derived from these data and is shown to be largely independent of the atom, in agreement with models of tunnel ionization. We compare the measurements with calculations in both the length gauge and the velocity gauge and show that the two gauges imply a different de Broglie wavelength.

Destructive interference during high harmonic generation in mixed gases

We report on the first experimental evidence of the destructive and constructive interference of high harmonics generated in a mixed gas of He and Ne, which facilitates the coherent control of high harmonic generation. Theoretically, we develop an analytical model of high harmonic generation in mixed gases and succeed in reproducing the experimental results and deriving the optimization conditions for the process. The observed interference modulation is attributed to the difference between the phases of the intrinsically chirped harmonic pulses from He and Ne, which leads to a novel method for broadband measurement of the harmonic phases and for observing the underlying attosecond electron dynamics.

Origin of anomalous spectra of dynamic alignments observed in N2 and O2

Recent pump-probe experiments with intense femtosecond laser pulses and diatomic molecules N2 and O2, have revealed the presence of Raman-forbidden anomalous series and lines in the Fourier spectrum of HHG (high harmonic generation) signals. A theoretical analysis of the problem is made by deriving a general expression of the angle dependent HHG operator that governs the dynamic alignment signals in linear molecules, and applying them to the experiments in N2 and O2. A unified interpretation of the origin of the observed Raman-allowed and the anomalous spectral features is given. The results are also used to estimate the molecular temperature in the experiments.

Direct XUV probing of attosecond electron recollision

We demonstrate that the recolliding electron wave packet, fundamental to many strong field phenomena, can be directly imaged with sub-A spatial and attosecond temporal resolution using attosecond extreme ultraviolet (XUV) pulses. When the recolliding electron revisits the parent ion, it can absorb an XUV photon yielding high energy electron and thereby providing a measurement of the electron energy at the moment of recollision. The full temporal evolution of the recollision wave packet can be reconstructed by measuring the photoelectron spectra for different time delays between the driving laser and the attosecond XUV probe. The strength of the photoelectron signal can be used to characterize the spatial distribution of the electron density in the longitudinal direction. Elliptical polarization can be used to characterize the electron probability in transversal direction.

Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light

We use counterpropagating light to directly observe the coherent buildup of high harmonic generation in a hollow waveguide geometry. We measure, for the first time, coherence lengths for high photon energies that cannot be phase matched using conventional approaches. We also probe the transition through phase matching, the ionization level at which different harmonic orders are generated, and the change in the coherence length as the driving laser is depleted. These results directly prescribe the optimal structures or pulse trains required for implementing quasiphase matching.

High harmonic generation and molecular orbital tomography in multielectron systems

High harmonic radiation is produced when atoms or molecules are ionized by an intense femtosecond laser pulse. The radiated spectrum has been shown experimentally to contain information on the electronic structure of the molecule, which can be interpreted as an image of a single molecular orbital. Previous theory for high harmonic generation has been limited to the single-active-electron approximation. Utilizing semisudden approximation, the authors develop a theory of the recombination step in high harmonic generation and tomographic reconstruction in multielectron systems, taking into account electron spin statistics and electron-electron correlations within the parent molecule and the ion. They show that the resulting corrections significantly modify the theoretical predictions, and bring them in a better agreement with experiment. They further show that exchange contributions to harmonic radiation can be used to extract additional information on the electronic wave function.

Transient phase masks in high-harmonic generation

We present a method for controlling the spatial properties of high-harmonic beams with high efficiency. The high nonlinearity of harmonic generation allows weak control beams to induce a phase mask for the extreme UV light as it is formed. We fabricate a phase grating and demonstrate efficient diffraction in the far field. Diffractive elements formed in this way are transient. Since they are induced by the subcycle interaction of the medium with the fundamental and control fields, they can be extended to the attosecond time scale.

Ellipticity dependence of high-order harmonic generation from aligned molecules

We report ellipticity dependence of high-order harmonic generation (HHG) from aligned N2, O2, and CO2 molecules. Experimentally, we find that the ellipticity dependence is sensitive to molecular alignment and to the shape and symmetry of the valence orbitals. It is also found that the destructive interference in the recombination process affects the ellipticity dependence. Theoretically, we extend the original Lewenstein model to a more generalized model, which can be applicable to HHG from molecules, by introducing an electron acceleration parameter xi(theta) and by combining the molecular orbital method. The present observations are successfully explained by our model.

Unified microscopic-macroscopic formulation of high-order difference-frequency mixing in plasmas

We investigate high-order difference-frequency mixing in plasmas, taking into account the microscopic rescattering physics and propagation effects for the first time. We show that phase matching can occur over a broad frequency range, up to very high photon energies, and that it is confined to specific temporal and spatial windows. This gated phase matching mechanism is driven by the continuous phase slip between two driving fields and can be employed for manipulating the temporal, spatial, and spectral properties of high harmonic emission.

Nonsequential double recombination in intense laser fields

A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cutoff are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cutoff is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.

Efficient isolated attosecond pulse generation from a multi-cycle two-color laser field

We present a new scheme to generate efficient isolated attosecond pulse by using the combination of a fundamental and a weak second harmonic (SH) field in the multi-cycle regime. Because of the symmetry breaking of the electric field, the ionization dynamics of the electron can be controlled by adjusting the relative phase of the two fields. Then attosecond (as) pulses will be generated each full optical cycle of the fundamental field. Our simulation shows that the intensity of the single attosecond pulse can be enhanced by an order of magnitude in our scheme compared with the scheme in [Opt. Lett. 31, 975 (2006)].

Scaling of wave-packet dynamics in an intense midinfrared field

A theoretical investigation is presented that examines the wavelength scaling from near-visible (0.8 micro m) to midinfrared (2 micro m) of the photoelectron distribution and high harmonics generated by a "single" atom in an intense electromagnetic field. The calculations use a numerical solution of the time-dependent Schrödinger equation (TDSE) in argon and the strong-field approximation in helium. The scaling of electron energies (lambda2), harmonic cutoff (lambda2), and attochirp (lambda -1) agree with classical mechanics, but it is found that, surprisingly, the harmonic yield follows a lambda -(5-6) scaling at constant intensity. In addition, the TDSE results reveal an unexpected contribution from higher-order returns of the rescattering electron wave packet.

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schrödinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.

Single attosecond pulses from high harmonics driven by self-compressed filaments

We show that isolated subfemtosecond, extreme ultraviolet (XUV) pulses can be generated via harmonic generation in argon by few-cycle infrared pulses formed through filamentation-induced self-compression in neon. Our calculations show that the time structure of the XUV pulses depends sensitively on both the amplitude and the phase modulation that are induced in the driving pulse during the self-compression process.

Generating single attosecond pulses via spatial filtering

The first observation of isolated attosecond pulses by Hentschel [Nature 414, 509 (2001)] resulted from an experiment that left the exact mechanism of their generation unresolved. A complete simulation of the experiment reveals the reason for its success: single pulses were efficiently isolated from two or more generated pulses by spatial filtering in the far field. Our explanation suggests a new, simple paradigm for the production of isolated attosecond bursts. We show that this method can be used, in conjunction with carrier-envelope phase stabilization, to select single attosecond pulses by use of 10 fs driving pulses.

Isolated Single-Cycle Attosecond Pulses

We generated single-cycle isolated attosecond pulses around approximately 36 electron volts using phase-stabilized 5-femtosecond driving pulses with a modulated polarization state. Using a complete temporal characterization technique, we demonstrated the compression of the generated pulses for as low as 130 attoseconds, corresponding to less than 1.2 optical cycles. Numerical simulations of the generation process show that the carrier-envelope phase of the attosecond pulses is stable. The availability of single-cycle isolated attosecond pulses opens the way to a new regime in ultrafast physics, in which the strong-field electron dynamics in atoms and molecules is driven by the electric field of the attosecond pulses rather than by their intensity profile.

Interferometric autocorrelation of an attosecond pulse train in the single-cycle regime

We report on the direct observation of the phase locking of the attosecond pulse train (APT) via interferometric autocorrelation in the extreme ultraviolet region. APT is formed with Fourier synthesis of high-order harmonic fields of a femtosecond laser pulse. Time-of-flight mass spectra of N+, resulting from the Coulomb explosion of N2 absorbing two photons of APT, efficiently yield correlated signals of APT. The measured autocorrelation trace exhibits that the duration of the pulse should be only 1.3 periods of the extreme ultraviolet carrier frequency. A few interference fringes within the short pulse duration clearly show two types of symmetry, which ensure the phase locking between pulses in APT.

Enhanced recollisions for antisymmetric molecular orbitals in intense laser fields

The peculiarities of antisymmetric molecular orbitals are investigated in very intense linearly polarized laser pulses. For this purpose, the ionization-recollision quantum dynamics is evaluated theoretically beyond the dipole approximation. As opposed to the usual situation, the laser magnetic field component is found to strongly enhance recollision probabilities for particularly oriented antisymmetric molecular orbitals. Harmonic generation and related processes are thus allowed at high laser intensities without the common limitations by the laser magnetic field.

High harmonic generation and molecular orbital tomography in multielectron systems: beyond the single active electron approximation

It was recently shown that the highest molecular orbital of N2 could be reconstructed from a series of high harmonic measurements. Existing theories of high harmonic generation and orbital tomographic imaging are based on the single active electron approximation that ignores essential quantum mechanical properties such as the indistinguishability of identical particles and the Pauli exclusion principle. We show that, when fully antisymmetrized multielectron wave functions and electronic relaxation in the cation are considered, molecular orbital tomography records the image of the Dyson orbital plus exchange contributions from inner shells. The mixing of contributions from more than one molecular orbital gives access to additional wave function information. By utilizing the exchange term, harmonic emission from a closed-shell 4-electron system can be interpreted as a complete Hartree-Fock wave function.

Monitoring molecular dynamics using coherent electrons from high harmonic generation

We report a previously undescribed spectroscopic probe that makes use of electrons rescattered during the process of high-order harmonic generation. We excite coherent vibrations in SF(6) using impulsive stimulated Raman scattering with a short laser pulse. A second, more intense laser pulse generates high-order harmonics of the fundamental laser, at wavelengths of approximately 20-50 nm. The high-order harmonic yield is observed to oscillate, at frequencies corresponding to all of the Raman-active modes of SF(6), with an asymmetric mode most visible. The data also show evidence of relaxation dynamics after impulsive excitation of the molecule. Theoretical modeling indicates that the high harmonic yield should be modulated by both Raman and infrared-active vibrational modes. Our results indicate that high harmonic generation is a very sensitive probe of vibrational dynamics and may yield more information simultaneously than conventional ultrafast spectroscopic techniques. Because the de Broglie wavelength of the recolliding electron is on the order of interatomic distances, i.e., approximately 1.5 A, small changes in the shape of the molecule lead to large changes in the high harmonic yield. This work therefore demonstrates a previously undescribed spectroscopic technique for probing ultrafast internal dynamics in molecules and, in particular, on the chemically important ground-state potential surface.

X-ray microprobe of orbital alignment in strong-field ionized atoms

We have developed a synchrotron-based, time-resolved x-ray microprobe to investigate optical strong-field processes at intermediate intensities (10(14) - 10(15) W/cm2). This quantum-state specific probe has enabled the direct observation of orbital alignment in the residual ion produced by strong-field ionization of krypton atoms via resonant, polarized x-ray absorption. We found strong alignment to persist for a period long compared to the spin-orbit coupling time scale (6.2 fs). The observed degree of alignment can be explained by models that incorporate spin-orbit coupling. The methodology is applicable to a wide range of problems.

Attosecond pulse trains generated using two color laser fields

We investigate the spectral and temporal structure of high harmonic emission from argon exposed to an infrared laser field and its second harmonic. For a wide range of generating conditions, trains of attosecond pulses with only one pulse per infrared cycle are generated. The synchronization necessary for producing such trains ensures that they have a stable pulse-to-pulse carrier envelope phase, unlike trains generated from one color fields, which have two pulses per cycle and a pi phase shift between consecutive pulses. Our experiment extends the generation of phase stabilized few cycle pulses to the extreme ultraviolet regime.

Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction

We demonstrate an extremely accurate method for measuring ultrabroadband, sub-10 fs pulses even if they exhibit a highly modulated spectrum, space-time coupling, or both. The method uses a spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction, which allows a zero additional phase measurement to be performed with a relatively low signal-to-noise ratio in real time and single shot.

Role of many-electron dynamics in high harmonic generation

High harmonic generation (HHG) in many-electron atoms is studied theoretically. The breakdown of the frozen-core single active electron approximation is demonstrated, as it predicts roughly the same radiation amplitude in all noble gases. This is in contradiction with experiments, where heavier noble gases are known to emit much stronger HHG radiation than lighter ones. This experimental behavior of the noble gases can be qualitatively reproduced when many-electron dynamics, within a simple approximation, is taken into account.

High-order harmonic generation from ions in a capillary discharge

We demonstrate a significant extension of the high-order harmonic cutoff by using a fully-ionized capillary discharge plasma as the generation medium. The preionized plasma dramatically reduces ionization-induced defocusing and energy loss of the driving laser due to ionization. This allows for significantly higher photon energies, up to 150 eV, to be generated from xenon ions, compared with the 70 eV observed previously. We also demonstrate enhancement of the harmonic flux of nearly 2 orders of magnitude at photon energies around 90 eV when the capillary discharge is used to ionize xenon, compared with harmonic generation in a hollow waveguide. The use of a plasma as a medium for high-order harmonic generation shows great promise for extending efficient harmonic generation to much shorter wavelengths using ions.

Adaptive spatial control of fiber modes and their excitation for high-harmonic generation

We present the control of high-harmonic generation (HHG) in hollow fibers using adaptive pulse shaping techniques. The shaping capabilities of our spatial light modulator (SLM) are demonstrated by the excitation of specific fiber modes inside a hollow fiber with a helium-neon laser. Afterwards spatially shaped ultrashort pulses are used to generate phase-matched high-harmonic radiation in a fiber. We show that by controlling the mode structure, we can manipulate the spatial and spectral properties of the generated harmonics.

Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 microm

We demonstrate an optical parametric chirped-pulse amplifier producing infrared 20 fs (3-optical-cycle) pulses with a stable carrier-envelope phase. The amplifier is seeded with self-phase-stabilized pulses obtained by optical rectification of the output of an ultrabroadband Ti:sapphire oscillator. Energies of -80 microJ with a well-suppressed background of parametric superfluorescence and up to 400 microJ with a superfluorescence background are obtained from a two-stage parametric amplifier based on periodically poled LiNbO3 and LiTaO3 crystals. The parametric amplifier is pumped by an optically synchronized 1 kHz, 30 ps, 1053 nm Nd:YLF amplifier seeded by the same Ti:sapphire oscillator.

Generation of high-energy self-phase-stabilized pulses by difference-frequency generation followed by optical parametric amplification

We produce ultrabroadband self-phase-stabilized near-IR pulses by a novel approach where a seed pulse, obtained by difference-frequency generation of a hollow-fiber broadened supercontinuum, is amplified by a two-stage optical parametric amplifier. Energies up to 20 microJ with a pulse spectrum extending from 1.2 to 1.6 microm are demonstrated, and a route for substantial energy scaling is indicated.

Three-step model for high-harmonic generation in many-electron systems

The three-step model (TSM) of high-harmonic generation (HHG) is generalized to atomic and molecular many-electron systems. Using many-body perturbation theory, corrections to the standard TSM due to exchange and electron-electron correlations are derived. It is shown that canonical Hartree-Fock orbitals represent the most appropriate set of one-electron states for calculating the HHG spectrum. To zeroth order in many-body perturbation theory, a HHG experiment allows direct access, in general, to a combination of occupied Hartree-Fock orbitals rather than to the highest occupied molecular orbital by itself.

Quantitative modeling of single atom high harmonic generation

It is shown by comparison with numerical solutions of the Schrödinger equation that the three step model (TSM) of high harmonic generation (HHG) can be improved to give a quantitatively reliable description of the process. Excellent agreement is demonstrated for the H atom and the H2(+) molecular ion. It is shown that the standard TSM heavily distorts the HHG spectra, especially of H2(+), and an explanation is presented for this behavior. Key to the improvement is the use of the Ehrenfest theorem in the TSM.

Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics

We demonstrate a new scheme for extreme ultraviolet (xuv) Fourier-transform spectroscopy based on the generation of two phase-locked high-harmonic beams. It allows us to measure for the first time interferograms at wavelengths as short as 90 nm, and open the perspective of performing high-resolution Fourier-transform absorption spectroscopy in the xuv. Our measurements also demonstrate that a precise control of the relative phase of harmonic pulses can be obtained with an accuracy on an attosecond time scale, of importance for future xuv pump-xuv probe attosecond spectroscopy.

Nonresonant ionization of oxygen molecules by femtosecond pulses: Plasma dynamics studied by time-resolved terahertz spectroscopy

We show that optical pump-terahertz probe spectroscopy is a direct experimental tool for exploring laser-induced ionization and plasma formation in gases. Plasma was produced in gaseous oxygen by focused amplified femtosecond pulses. The ionization mechanisms at 400- and 800-nm excitation wavelengths differ significantly being primarily of a multiphoton character in the former case and a strong-field process in the latter case. The generation of the plasma in the focal volume of the laser and its expansion on subnanosecond time scale is directly monitored through its density-dependent susceptibility. A Drude model used to evaluate the plasma densities and electron-scattering rates successfully captures the observations for a wide range of pump intensities. In addition, rotational fingerprints of molecular and ionic species were also observed in the spectra.

Optical high harmonic generation in C60

High harmonic generation (HHG) requires a strong laser field, but in C60 a relatively weak laser field is sufficient. Numerical results presented here show that, while its low order harmonics result from the laser field, its high order ones are mainly from the multiple excitations. Since high order harmonics directly correlate with electronic transitions, the HHG spectrum accurately measures transition energies. Therefore, C60 is not only a promising material for HHG, but may also present an opportunity to develop HHG into an electronic structure probing tool.

Frequency-sheared, time-delayed extreme-ultraviolet pulses produced by high-harmonic generation in argon

We report the production of frequency-sheared high harmonics in argon by control of the envelope and chirp of the electric field of the femtosecond driving laser pulse. Using the classic three-step model of high-harmonic generation, we established a direct link between the properties of the harmonics and the fully characterized driving pulses. A simulation of the single-atom response in the strong-field approximation confirms the simple picture and shows good agreement with the experimental results.

Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors

In the race toward attosecond pulses, for which high-order harmonics generated in rare gases are the best candidates, both the harmonic spectral range and the spectral phase have to be controlled. We demonstrate that multilayer extreme-ultraviolet chirped mirrors can be numerically optimized and designed to compensate for the intrinsic harmonic chirp that was recently discovered and that is responsible for temporal broadening of pulses. A simulation shows that an optimized mirror is capable of compressing the duration from approximately 260 to 90 as. This new technique is an interesting solution because of its ability to cover a wider spectral range than other technical devices that have already been proposed to overcome the chirp of high harmonics.

Measurement of harmonic phase differences by interference of attosecond light pulses

By using a self-referencing technique, we have experimentally measured the influence of the carrier-envelope phase of femtosecond light pulses on the phase of the electric field of the radiation produced by high-order harmonic generation. We show that, in particular experimental conditions, the temporal evolution of the electric field of the attosecond pulses, is directly controlled by the carrier-envelope phase of the driving pulses.

Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity

We demonstrate the generation of phase-coherent frequency combs in the vacuum utraviolet spectral region. The output from a mode-locked laser is stabilized to a femtosecond enhancement cavity with a gas jet at the intracavity focus. The resulting high-peak power of the intracavity pulse enables efficient high-harmonic generation by utilizing the full repetition rate of the laser. Optical-heterodyne-based measurements reveal that the coherent frequency comb structure of the original laser is fully preserved in the high-harmonic generation process. These results open the door for precision frequency metrology at extreme ultraviolet wavelengths and permit the efficient generation of phase-coherent high-order harmonics using only a standard laser oscillator without active amplification of single pulses.

Quantum interference during high-order harmonic generation from aligned molecules

High-order harmonic generation (HHG) from atoms and molecules offers potential application as a coherent ultrashort radiation source in the extreme ultraviolet and soft X-ray regions. In the three-step model of HHG, an electron tunnels out from the atom and may recombine with the parent ion (emitting a high-energy photon) after undergoing laser-driven motion in the continuum. Aligned molecules can be used to study quantum phenomena in HHG associated with molecular symmetries; in particular, simultaneous observations of both ion yields and harmonic signals under the same conditions serve to disentangle the contributions from the ionization and recombination processes. Here we report evidence for quantum interference of electron de Broglie waves in the recombination process of HHG from aligned CO2 molecules. The interference takes place within a single molecule and within one optical cycle. Characteristic modulation patterns of the harmonic signals measured as a function of the pump-probe delay are explained with simple formulae determined by the valence orbital of the molecules. We propose that simultaneous observations of both ion yields and harmonic signals can serve as a new route to probe the instantaneous structure of molecular systems.

Second order autocorrelation of an XUV attosecond pulse train

Temporal widths of an attosecond (asec) XUV radiation pulse train, formed by the superposition of higher order harmonics, have been recently determined utilizing a 2nd order autocorrelation measurement. An assessment of the validity of the approach, for the broadband XUV radiation of asec pulses, is implemented through ab initio calculations modeling the spectral and temporal response of the two-XUV-photon He ionization detector employed. The measured width of the asec bursts is discussed in terms of the spectral phases of the individual harmonics, as well as in terms of the spatially modulated temporal width of the radiation, and is found in reasonable agreement with the expected duration.